In addition to the extra baryon charge density \(q_B^{\rm dec}\) , we therefore also obtain an extra contribution to the lepton charge density of equal size, \(q_L^{\rm dec} = q_B^{\rm dec}\) .
At the same time, the hypermagnetic field is transformed into the usual magnetic field of electromagnetism, which means that no hypermagnetic helicity that would be capable of sourcing a baryon asymmetry survives after the EWPT.
Meanwhile, the magnetic field emanating from the EWPT does remain helical.
But instead of hypermagnetic helicity, it now features magnetic helicity, which is of phenomenological interest in its own right,\(16\endcsname \)Similar to hypermagnetic fields, maximally helical magnetic fields experience an “inverse cascade” evolution in the turbulent regime (see also Sec. ), which can lead to strong present-day magnetic fields with large coherence length in cosmic voids [1]}, [2]}, [3]}.
The search for and a possible hint of helical intergalactic magnetic fields, based on the parity-odd correlation functions of diffuse gamma rays emitted by blazars, is discussed, e.g., in Refs. [4]}, [5]}, [6]}, [7]} (see also Ref. [8]}).
The \(\eta _\chi \)  values required for successful baryogenesis after axion inflation, however, lead to magnetic fields that are not strong enough to explain these blazar observations [9]}, [10]}.

even if it is no longer relevant for the evolution of the baryon asymmetry.
In panel (e) of Fig. REF , we indicate this behavior of the helicity density by setting the CS charge-to-photon ratio \(\eta _{\rm CS}\)  to zero towards the end of the EWPT, which completes our discussion of Fig. REF .
